32 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , B EIJING 2011Rigidity dependence of the solar-wind-effect on cosmic-ray intensities associated with Solar activity
H. KOJIMA1 , S. S HIBATA2 , A. O SHIMA 3 , H. TAKAMARU2 , H. M. A NTIA4 , S. R. D UGAD4 , T. F UJII5 , S. K. G UPTA4 ,Y. H AYASHI5 , N. I TO5 , A. I YER4 , P. JAGADEESAN4 , A. JAIN4 , S. K AWAKAMI5 , K. K URAMOTO5 , D. M ATSUMIYA5 ,T. M ATSUYAMA 5 , M. M INAMINO5 , P. K. M OHANTY 4 , I. M ORISHITA6 , S. D. M ORRIS4 , P. K. NAYAK4 ,T. N ONAKA7 , S. O GIO5 , T. O KUDA5 , B. S. R AO4 , K. C. R AVINDRAN4 , K. S IVAPRASAD4 , P. S UBRAMANIAN4 ,H. TANAKA5 , S. C. T ONWAR4 , Y. YAMASHITA5 , K. YAMAZAKI51
Faculty of Engineering, Aichi Institute of Technology, Toyota, Aichi, 470-0392, Japan
2
College of Engineering, Chubu University, Kasugai, Aichi, 487-8051, Japan
3
National Astronomical Observatory of Japan, Mitaka, Tokyo, 181-8588, Japan
4
Tata Institute of Fundamental Research, Homi Bhabha Road, Munbai, 400005, India
5
Graduate School of Science, Osaka City University, Sumiyoshi, Osaka, 558-8585, Japan
6
Department of Information Management, Asahi University, Hozumi, Gifu, 501-0296, Japan
7
Institute for Cosmic Ray Research, University of Tokyo, Kashiwa, Chiba, 277-8582,Japan
shibata@isc.chubu.ac.jp
DOI: 10.7529/ICRC2011/V11/0982
Abstract: We presented the Solar activity dependence of the solar-wind-effect on cosmic ray intensity variations at 30thICRC. At that time, we showed the results obtained mainly by using the data of Kiel neutron monitor and Nagoya muon
telescope. We now utilise the data of large GRAPES-3 tracking muon telescope collected during 9 years from 2000 to2008. From the ﬁeld of view of this telescope, we obtained the cosmic ray intensities corresponding to the median rigidityfrom 64.4 to 92.0 GV. We have investigated the rigidity dependence of the solar-wind-effect using this data together withthe data of neutron monitors at Keil (17.2 GV) and at Mexico City (25.8 GV) for lower rigidity, and these are discussed
in detail.
Keywords: Cosmic ray intensity variations, Solar-wind-effect, Solar activity dependence, Rigidity dependence, Solar
modulation

1

Introduction

According to the diffusion-convection theory [1] [2] [3] [4],it is expected that the cosmic ray intensity varies with thesolar wind velocity. If their relationship is quantitatively
clariﬁed, it will become observationally possible to obtain
the diffusion coefﬁcient for the propagation of galactic cosmic rays ﬂown into the heliosphere from inter stellar space.
Since the beginning of direct measurements of solar windwith satellites (Oct. 1963), there have been several studies[5] [6] [7] that had pointed out the effect of solar wind on
the variations of the cosmic ray intensities, so called thesolar-wind-effect; i.e. the intensity of cosmic rays decreases as the velocity of solar wind increases. These analyses have mainly concentrated on the relationship between
time variations of the cosmic ray intensities and high speed
streaming of the solar wind. There have been few analyses
that have clariﬁed the quantitative relationship between theintensity variation of the cosmic rays and the velocity variation of the steady state solar wind. Especially, the rigidity

dependence of the solar-wind-effect has seldom been studied.
The difﬁculty of the analysis is mainly due to following reason. Since the intensity of cosmic rays varies with several
causes, it shows a very complicated time proﬁle which iscomposed of many different variations with different timeperiods. For example, it contains a long term intensity variation of eleven-year period. Transient variations like Forbush decreases are also contained. There also exist the intensity variation of cosmic rays caused by the anisotropy
due to the earth’s rotation or revolution around the sun. In
our observation, the intensity variation of the cosmic rays
has been recoded as the mixture of these different phenomena.
As for the variation of the solar wind velocity, it is also
known that there exist several components of the variationsuch as a high speed ﬂow accompanied by a solar ﬂare, arecurrent variation with a period of around 27 days (13.5days) corresponding to the solar rotation, or a long termvariation with a period of several years.

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Thus for the both of variations of the cosmic ray intensity
and the solar wind velocity, it is very difﬁcult to separate
each component of variation with different cause in a simple way. Then we are not always able to obtain an acceptable result from a simple correlation analysis between thesedata of the cosmic ray intensity and the solar wind velocity
in an extended period.
In our previous investigations [8] [9] [10], we have successfully shown the solar-wind-effect on the intensity variationof cosmic rays by removing both the long term variations and the transient ones which might cause the problems
described above, then we have obtained the clear dependence of the solar-wind-effect on the Solar activity. In thispaper, we extend these analysis to examine the rigidity dependence of the solar-wind-effect and the year-to-year variation of it by using the same ﬁltering method which will be
described in the next section.

2Analysis and Result

In order to investigate the rigidity dependence of the solarwind-effect, the data of cosmic ray intensity observed by
the GRAPES-3 tracking muon telescope with large effective area and ﬁne angular resolution of seven degree areused. This telescope consists of 16 modules with the effective area of 35 m2 for each and is installed at Ooty in southern India near equator (76◦ 40 E, 11◦ 23 N, 2200 m asl). In
1998, we have started to observe the time variation of muon
intensity with this telescope and the incident direction ofeach muon have been recorded since Apr., 1999. For theanalysis described here, we utilise the data of this telescopemeasured during 9 years from 2000 to 2008. The data observed by the neutron monitors at Kiel and at Mexico City
during the corresponding period are also used. Solar windvelocities we used are referred to the OMNI 2 data set.

2.1

Component
NENNW
EVWSESSW
Kiel NMMexico City NM

Rigidity (GV)
92.0
73.5
73.2
82.9
66.3
64.4
88.7
69.970.917.2
25.8

Table 1: Median rigidities of the data.

Median rigidities of the data

The GRAPES-3 tracking muon telescope detects muons ofenergy above 1 GeV. The ﬁeld of view of the telescopeconsists of 15 × 15 = 225 direction bins as shown in Fig.1.
For the analysis, we adopted the inner 13 × 13 = 169 bins as the effective ﬁeld of view and reconﬁgured them intonine bins labeled as NE, N, NW, E, V, W, SE, S, and SW
according to the incident direction of muons shown in thesame ﬁgure. The median rigidity of corresponding primary
proton to each bin was estimated from Monte Carlo simulations carried out using CORSIKA package. The values of
median rigidities thus calculated are listed in Table1. Therigidities of neutron monitors derived from the coupling coefﬁcients [11] are also shown in the same table.

2.2

Figure 1: The ﬁeld of view of the GRAPES-3 tracking
muon telescope.

Data processing

In this analysis, the method of data processing we adopted
is similar to that reported at the 30th and 31st ICRCs [8] [9][10]. At ﬁrst, for the data of the GRAPES-3 tracking muon
telescope, the number of muons collected for one hour is
combined for each of nine bins. Thereafter, the hourly
muon rate expressed as fractional percentage change fromthe average of the entire data set for the corresponding bin
are obtained. Next, the hourly rate is corrected for changes
in the atmospheric pressure. Then, for each bin, the datawith values exceed ten times of the root mean square arerejected as abnormal. For the data of neutron monitors,
the hourly counting rate is also converted to the fractional
percentage change from the average of the entire data set.
The same rejection criteria for abnormal as above is also
applied to the data of neutron monitors.
After those processes, in order to reject some kinds of interference between several variations caused by the different
origins described in the previous section, the data are treated as the following way. The duration of a transient event,such as a Forbush decrease, is estimated using the daily av-Vol. 11, 214

32 ND I NTERNATIONAL C OSMIC R AY C ONFERENCE , B EIJING 2011

Figure 2: Year-to-year variation of the regression coefﬁcients of cosmic-ray intensities vs solar wind velocities (forthe data of the GRAPES-3 tracking muon telescope).

Figure 3: Year-to-year variation of the regression coefﬁcients of cosmic-ray intensities vs solar wind velocities (forthe all data).

eraged counting rate of the Kiel neutron monitor. The daywith the rate less than −4 % compared to the average ofthe three preceding days is presumed as a day in a transient
event, and the corresponding data are rejected. For the indication of the recovery after the transient event, more than
70 % from the minimum rate is required. After this, the differences from 648-hour (27-day) running average are taken
to remove the long term effects in both the data of cosmic
ray intensity and the solar wind velocity. Then, daily averages of all the data are obtained from hourly counting rates
processed as above.

2.5

2.3

Regression analysis

To get the year-to-year variation of the solar-wind-effecton cosmic-ray intensities, the regression analysis of thecosmic-ray intensities vs solar wind velocities is done year
by year from 2000 to 2008 on daily basis. The regression
coefﬁcients obtained are around −0.0010 %/(km/s) fornine bins of the GRAPES-3 tracking muon telescope andaround −0.0025 %/(km/s) for neutron monitors as shownin Figures 2 and 3. In Fig.2, the regression coefﬁcients obtained only from the data of the GRAPES-3 tracking muon
telescope are shown. The regression coefﬁcients obtained
form the data of neutron monitors are combined in Fig.3.

2.4

Rigidity dependence of the solar-wind-effect

As noticed in the previous subsection, the magnitudes ofregression coefﬁcients derived from the data of neutron
monitors are about the twice as large as those derived fromthe data of the GRAPES-3 tracking muon telescope. Thismeans that there exist the rigidity dependence of the solarwind-effect on cosmic-ray intensities. In Figures 4 and 5,
the regression coefﬁcients are re-plotted with a new abscissa of corresponding median primary rigidities given in
Table1. From these ﬁgures, you can easily see the rigidity dependence. For the guide of eyes, the regression lines
for the data points plotted in Fig.5 are separately drawn inFig.6. From the ﬁgure, as far as observing the inclinationsof the lines correspond to 2001, 2003, 2005, there seems tobe the Solar activity dependence. However, the relation becomes not so simple when the line of 2007 is included. So,

Solar activity dependence of the solar-windeffectThough this is a reconﬁrmation of our previous results [8][9], the Solar activity dependence of the solar-wind-effecton cosmic-ray intensities can be seen from Fig.2 or Fig.3.
The correlation between the regression coefﬁcients and theSolar activity indices such as the sunspot numbers is negative, i.e. the magnitudes of regression coefﬁcients are large
before 2004 (active term) and small after 2004 (quiet term),
and the ratio of coefﬁcients is about 2 (see also [9]).

Figure 4: Rigidity dependence of the regression coefﬁcients of cosmic-ray intensities vs solar wind velocities (forthe data of the GRAPES-3 tracking muon telescope).

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H. KOJIMA et al. R IGIDITY DEPENDENCE OF THE SOLAR - WIND - EFFECT ON COSMIC - RAY INTENSITIES ASSOCIATED WITHS OLAR ACTIVITY

large before 2004 (active term) and small after 2004 (quietterm).
The rigidity dependence of the solar-wind-effect are clearlyobserved by this analysis, but the existence of their Solar
activity dependency is inconclusive at this time.

Acknowledgements

Figure 5: Rigidity dependence of the regression coefﬁcients of cosmic-ray intensities vs solar wind velocities (forthe all data).

Figure 6: Regression lines of the data points for odd years
shown in Fig.5 (2001, 2003, 2005, 2007).
at this time, the existence of their Solar activity dependency
is inconclusive.

3Conclusion

In this paper, the existence of the solar-wind-effect on
cosmic-ray intensity variations is conﬁrmed and the regression coefﬁcients around −0.0010 %/(km/s) are obtainedusing the data of GRAPES-3 tracking muon telescope observed during 9 years from 2000 to 2008. From the yearto-year regression analyses, we can deduce the Solar activity dependency of the solar-wind-effect. The correlation isnegative, and the magnitudes of regression coefﬁcients areThe authors express our thanks to the staff of the neutron
monitor stations at Kiel and at Mexico City for providing
the cosmic ray data used in this analysis. The staffs of Space Physics Data Facility (SPDF) and National Space Science Data Center (NSSDC) are also acknowledged for allowing us to use the data in OMNI 2 data set.
This work is partly supported by the grant in aid of theSolar Terrestrial Environment Laboratory of Nagoya University and the Institute for Cosmic Ray Research of University of Tokyo.

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